There are greatly varying approaches for the industrial production of bevel gears. Crown gears, as a special form of bevel gears, are frequently produced by a plunging method (also called piercing), in which the profile is generally accurately imaged as a tooth gap in the material of a crown gear workpiece. A corresponding example is shown in schematic form in FIGS. 1A, 1B, and 1C.
This plunging method is a forming method. There are both single-indexing and also continuous-indexing plunging or forming methods. The tool 2 (a cutter head gear-cutting tool 2 here) having bar cutters 3 executes solely a plunging or piercing movement ET in relation to the crown gear workpiece 1 for the milling of the tooth gaps. Most of the methods in this case operate in the two-flank cut, also called completing. In this case, both tooth flanks are finished using one tool and one machine setting (as described in one of the following paragraphs). There are also plunging methods in which the individual flanks are machined separately. However, this is only rarely used in practice.
The workpiece spindle axis R2 (also called the workpiece rotational axis R2) is typically inclined in relation to the tool spindle axis R1 (also called the tool rotational axis R1), as indicated in FIGS. 1A and 1B. FIG. 1A shows the situation during the execution of an infeed movement ZB, to move the tool 2 toward the crown gear workpiece 1. FIG. 1B shows a snapshot after the execution of the plunging movement ET. During the plunging, the machine setting of the gear-cutting machine is maintained in the simplest case, since in this case only a linear plunging or piercing movement ET of the tool 2 into the crown gear workpiece 1 takes place. In this case, there is only the plunging advance, which is illustrated in the basic gear-cutting machine by the movement of only one axis. Depending on the construction of the real gear-cutting machine, however, multiple axes of the machine can move. Further details in this regard can be inferred, for example, from document DE10334493 A1.
FIG. 1C illustrates the known plunging method in simplified schematic form in summary. The dotted arrow illustrates the infeed movement ZB and the solid arrow, which is oriented in the direction of the crown gear workpiece 1 (not shown here), illustrates the plunging movement ET. A dashed arrow having reversed direction is shown in parallel to the solid arrow. This dashed arrow illustrates the withdrawal movement AT. After the tooth base of a tooth gap to be created is reached, a direction reversal takes place. In FIG. 1C, this is shown by the opposing arrows ET and AT and by the reversal point UP. The orientation of the infeed movement ZB does not necessarily have to correspond to the orientation of the plunging movement ET, as shown in FIG. 1C. The symbol M1 is to indicate that the plunging takes place using a first machine setting M1.
The machine setting during the plunging is typically defined by the following variables: radial distance φ (also referred to as radial), cradle angle α, machine base angle γ, depth position χ, axial offset η, inclination angle (tilt) τ and orientation angle (swivel) σ, and the distance mccp of the axis intersection point of the crown gear workpiece 1 from the machine center of the gear-cutting machine. All of these variables can be constant during the plunging, as already described. Only the depth position χ changes, as indicated in FIG. 1B by the arrow ET.
Further details on the plunging of bevel gears can be inferred, for example, from the book “Kegelräder; Grundlagen, Anwendungen [bevel gears; foundations, applications]” of the editor Jan Klingelnberg, 2008, Springer-Verlag, (see, for example, pages 105-106 therein).
Alternatively, crown gears can also be produced by generative methods. In most cases, however, plunging is more productive than generative methods.
It has been shown that topography errors, such as spiral angle, longitudinal crowning, vertical crowning, twist, and flank angle errors can occur in plunge-machined bevel gears 1, i.e., in bevel gears 1 which have been machined by a plunging method. Moreover, tooth thickness and indexing errors can occur. The flank angle errors and the correction thereof are primarily described hereafter, wherein the disclosure herein may also be applied to the other mentioned errors.
Studies have now shown that these flank angle errors are caused, for example, by thermal influences in the gear-cutting machine and by deformations of the crown gear workpieces. Variations, which occur during the regrinding of the bar cutters of the cutter head gear-cutting tools 2, have been identified as a further cause of the occurrence of flank angle errors.
The location, direction, or shape of the mentioned flank angle errors can be defined as positive and negative. They can occur oriented in opposite directions, i.e., the flank angle error of the concave tooth flank has a different sign than that of the convex tooth flank, or oriented in the same direction, the flank angle errors of both tooth flanks have the same sign. Such flank angle errors, which either point in the positive direction on both tooth flanks or in the negative direction on both tooth flanks, cannot be corrected to zero during the plunging by means of correction of the machine settings, since the plunging, as mentioned above, machines the concave and convex tooth flanks using only one machine setting. Because only one machine setting is usually available during the plunging, such flank angle errors can only be averaged via changing the plunging position. However, this is only possible if the flank angle errors are different from the absolute value. The relative position between the gear-cutting tool 2 and the crown gear workpiece 1 is referred to as the plunging position.